Simple Push-relabel Algorithms for Matroids and Submodular Flows

A fast cost scaling algorithm for submodular flow

This paper presents the current fastest known weakly polynomial algorithm for the submodular flow problem when the costs are not too big. It combines Röck’s or Bland and Jensen’s cost scaling algorithms, Cunningham and Frank’s primal-dual algorithm for submodular flow, and Fujishige and Zhang’s push-relabel algorithm for submodular maximum flow to get a running time of O(nh logC), where n is th...

A push-relabel framework for submodular function minimization and applications to parametric optimization

Recently, the first combinatorial strongly polynomial algorithms for submodular function minimization have been devised independently by Iwata, Fleischer, and Fujishige and by Schrijver. In this paper, we improve the running time of Schrijver’s algorithm by designing a push-relabel framework for submodular function minimization (SFM). We also extend this algorithm to carry out parametric minimi...

A Push-Relabel Framework for Submodular Function Minimization and Applications to Parametric Optimization

Two-Level Push-Relabel Algorithm for the Maximum Flow Problem

We describe a two-level push-relabel algorithm for the maximum flow problem and compare it to the competing codes. The algorithm generalizes a practical algorithm for bipartite flows. Experiments show that the algorithm performs well on several problem families.

Experiments on Push-Relabel-based Maximum Cardinality Matching Algorithms for Bipartite Graphs

We report on careful implementations of several push-relabel-based algorithms for solving the problem of finding a maximum cardinality matching in a bipartite graph and compare them with fast augmentingpath-based algorithms. We analyze the algorithms using a common base for all implementations and compare their relative performance and stability on a wide range of graphs. The effect of a set of...